On a mixed problem for the parabolic Lame type operator

Описание

Тип публикации: статья из журнала

Год издания: 2015

Идентификатор DOI: 10.1515/jiip-2014-0043

Ключевые слова: Boundary value problems for parabolic equations, ill-posed problems, integral representation's method, Boundary value problems, Newtonian liquids, Cylindrical domain, Ill posed problem, Integral representation, Parabolic Equations, Smooth functions, Solvability conditions, Uniqueness theorem, Vector functions, Navier Stokes equations

Аннотация: We consider a boundary value problem for a Lame type operator, which corresponds to a linearisation of the Navier-Stokes' equations for compressible flow of Newtonian fluids in the case where pressure is known. It consists of recovering a vector function, satisfying the parabolic Lame type system in a cylindrical domain, via its vaПоказать полностьюlues and the values of the boundary stress tensor on a given part of the lateral surface of the cylinder. We prove that the problem is ill-posed in the natural spaces of smooth functions and in the corresponding Holder spaces; besides, additional initial data do not turn the problem to a well-posed one. Using the integral representation's method we obtain a uniqueness theorem and solvability conditions for the problem. We also describe conditions, providing dense solvability of the problem.

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Издание

Журнал: JOURNAL OF INVERSE AND ILL-POSED PROBLEMS

Выпуск журнала: Vol. 23, Is. 6

Номера страниц: 555-570

ISSN журнала: 09280219

Место издания: BERLIN

Издатель: WALTER DE GRUYTER GMBH

Авторы

  • Puzyrev Roman (Siberian Fed Univ, Inst Math & Comp Sci, Krasnoyarsk 660041, Russia)
  • Shlapunov Alexander (Siberian Fed Univ, Inst Math & Comp Sci, Krasnoyarsk 660041, Russia)

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